Template 1
Math III · N-CN.8
Extend polynomial identities to complex numbers for higher-degree polynomial work.
Extend polynomial identities to complex numbers for higher-degree polynomial work.
Concept
Number and Quantity
Domain
The Complex Number System
Problem Types
Problem Templates In This Objective
10 problem types are attached to this objective. The full web app handles practice, answers, hints, and walkthroughs.
Template 2
Factor an even-power polynomial completely over the complex numbers using conjugate imaginary factors
Template 3
Factor a cube polynomial over R and C and list roots
Template 4
Multiply complex conjugate linear factors to write a real polynomial
Template 5
Verify a complex zero of a real-coefficient polynomial using conjugate factors
Template 6
Find all complex roots of an already factored polynomial, including roots from a quadratic that gives a conjugate imaginary pair
Template 7
Build the unique monic real polynomial from roots
Template 8
Solve a polynomial over the complex numbers by factoring and using conjugate complex factors
Template 9
Compare complete factorization over R and C
Template 10